A physics-informed deep learning paradigm for car-following models

Graph attention network for Car‐Following Model under game between desired and real state

“…And, the experimental results show that the error of simple backpropagation neural network is smaller than Gipps and Wiedemann74. Mo et al [17] combined deep learning with the IDM or OVM respectively to jointly predict the state of following vehicle at time t + Δ𝜏. All the above studies have obtained good simulation results, which proves that only the information at time t can be used as the input to obtain high simulation accuracy.…”

“…At the same time, the trained GATCF model and FNN model are used to simulate the driving trajectory of the following vehicle. The RMSE i p and MAE i p are used to calculate the simulation error of the i-th vehicle, as shown in Equations ( 16), (17). The mean and standard deviation of the simulation errors of each model were calculated separately, as shown in Table 7.…”

“…In Figure 8, the trajectory data of the vehicle whose 'Vehicle ID' is equal to 396 is drawn with a black solid line, the real trajectory data of the remaining vehicles is drawn with a grey solid line, and the simulated trajectory data is drawn with a blue dotted line. Apply Equations ( 16), (17) to calculate the simulation error of the i-th vehicle, and calculate the average simulation error of each vehicle as shown in Table 9. As shown in the statistical results in Table 9, the RMSE error of the GATCF model proposed in this paper is 5.3391, and the MAE is equal to 3.9638, which is smaller than the simulation errors of Gipps, OVM, IDM, and FNN.…”

“…Mo et al. [17] combined deep learning with the IDM or OVM respectively to jointly predict the state of following vehicle at time $$t + \Delta \tau $$. All the above studies have obtained good simulation results, which proves that only the information at time t can be used as the input to obtain high simulation accuracy.…”

A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation

“…Yuan et al [33] proposed to leverage a hybrid framework, physics regularized Gaussian process [34] for macroscopic traffic flow modeling and TSE. The hybrid methods using the PIDL framework [35], [36], [37] recently becomes an active field. Huang et al [38] studied the use of PIDL to encode the Greenshields-based LWR and validated it in the loop detector scenarios using SUMO simulated data.…”